Actually modern fridges are usually less efficient. But that's because they use refrigerants that are literally thousands of times less harmful to the environment.

Old appliances frequently used R-12 which is an damn nice refrigerant except it depleted ozone and has a GWP (global warming potential) of 10,900. That means 1lb of R12 released into the air causes the same amount of global warming as releasing 10,900 lbs of CO2.

Newer appliances use refrigerants like R134a which still works pretty well, doesn't deplete ozone, and only has a GWP of 1,430.

The newest appliances are more frequently using R-600a which is hard on compressors because it has a high head pressure and it doesn't cool quite as well. But it also doesn't deplete ozone and it has a GWP of just 3. The bigest downside of that one is that it's very flamable (it's isobutane) so the legal limit on how much residential appliances can us is very low.